The present invention relates to an apparatus which receives signals transmitted from position-fixing satellites by a plurality of antennas and determines the relative positions of the antennas based on carrier phases of the signals received.
Conventionally, a carrier phase-based relative positioning apparatus which receives radio signals transmitted from satellites of the global positioning system (GPS) by a plurality of antennas disposed at specific positions with one of the antennas being used as a reference antenna, and measures carrier phases of the radio signals to determine the positions of the antennas with respect to the reference antenna with high accuracy is used in a system for determining the relative position of a mobile unit with high accuracy or in a system for detecting the moving direction and attitude of a mobile unit, for example.
One important factor in carrier phase-based relative positioning technology is how correctly the integer ambiguity of the carrier phases should be determined. When determining a single difference phase between radio signal carrier phases at antenna positions based on radio signals transmitted from one satellite and received by two antennas, or when determining a double phase difference from a pair of single phase differences derived from radio signals transmitted from two satellites and received by two antennas, a directly measurable value is the carrier phase of the received radio signal up to 360xc2x0, and it is necessary to determine the integer ambiguity using other method than direct observation.
In principle, the integer ambiguity is determined by choosing possible candidates of the true integer ambiguity, screening the candidates by use of various test methods, and selecting the eventually remaining one candidate as the integer ambiguity.
More specifically, the candidates are conventionally assessed by the following methods.
(1) Assessment Using Baseline Length
It the baseline length between a pair of antennas is known, multiple candidates are evaluated depending on whether an observed baseline length matches the actual baseline length within a specified degree of accuracy.
(2) Assessment Using Residual Sum of Squares
Residues, or the differences between observed phase differences and an estimated phase difference obtained by calculation, are determined and a "khgr"2-test is conducted using the sum of squares of the residues.
(3) Assessment Using Inner Product
If there are two or more baselines and the positions of antennas have a fixed relationship, the inner product of each pair of baselines is fixed. Using this relationship, the inner product of each pair of baselines obtained from candidates is calculated and the candidates are evaluated based on a comparison between the calculated inner product and the inner product of actual baselines.
(4) Assessment Based on Whether There Exists Only One Set of Good Integer Ambiguities
Naturally, only one true integer ambiguity exists for one baseline. If one set of integer ambiguities is left after conducting some of the testing methods mentioned above, it is selected as the true integer ambiguities.
It is generally possible to determine true integer ambiguities within a reasonably short period using some of the aforementioned testing methods of the prior art. Under certain conditions, however, the conventional carrier phase-based relative positioning apparatus may happen to output considerably erroneous relative positioning results despite the fact that the obtained integer ambiguity is incorrect. Also if more than one candidate passes the aforementioned tests, it would not be possible to eventually determine the true integer ambiguity.
In view of the foregoing, it is an object of the invention to solve the aforementioned problems of the prior art by using a new testing method. It is a more specific object of the invention to provide a carrier phase-based relative positioning apparatus which is capable of improving the reliability of calculated integer ambiguities, shorten the time required for determining one set of correct integer ambiguities from a plurality of candidates, and make a more reliable judgment on a cycle slip which could occur even after determining correct integer ambiguities.
In one aspect of the invention, a carrier phase-based relative positioning apparatus comprises a plurality of antennas of which at least one is installed on a mobile unit, means for determining the relative positions of each pair of the multiple antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with the multiple antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined based on whether the relative positions of the antennas fall in a preset range in which the relative positions will fall under normal conditions.
In this construction, if the relative positions of the antennas determined from the calculated integer ambiguity do not fall in the preset range when the range in which the relative positions will fall under normal conditions is known, the integer ambiguity is regarded as being incorrect. On the contrary, if the relative positions of the antennas fall in the preset range, the integer ambiguity is regarded as a candidate of the true integer ambiguity.
In another aspect of the invention, a carrier phase-based relative positioning apparatus comprises a plurality of antennas of which at least one is installed on a mobile unit, means for determining the attitude of a baseline vector between at least two of the multiple antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with the multiple antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined based on whether the attitude falls in a preset range in which the attitude will fall under normal conditions.
In one practical application, the multiple antennas are installed on a vessel or an aircraft, and if attitude angles determined from the calculated integer ambiguity are unrealistic and can not be normally taken by the vessel or the aircraft, the integer ambiguity is regarded as being incorrectly determined,
In the above construction, the baseline vector between two antennas provides one attitude angle of the mobile unit. If three antennas are used, two baseline vectors between them give two attitude angles respectively. When four antennas are used, they provide more than one pair of baseline vectors. In this case, attitude angles can be obtained from the individual pairs of baseline vectors. Then, a judgment may be made to determine whether each of the attitude angles falls in its normal range or, using part of the multiple baseline vectors or all of them, a judgment may be made to determine whether the optimum (or apparently the most reliable) attitude angle falls in the normal range.
In still another aspect of the invention, a carrier phase-based relative positioning apparatus comprises a plurality of antennas of which at least one is installed on a mobile unit, means for determining the attitude of the mobile unit from the relative positions of two of the multiple antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with the multiple antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined by comparing the aforesaid attitude with the attitude of the mobile unit measured by an attitude measuring device without using the radio signals from the position-fixing satellites and judging whether the difference between the two attitudes fall in a preset range in which the difference between both will fall under normal conditions.
Since attitude angles are determined regardless of the determination of the integer ambiguity, the integer ambiguity is regarded as being incorrectly determined if the attitude angles obtained from relative positioning of carrier phases greatly differ from attitude angles obtained by the attitude measuring device.
In still another aspect of the invention, a carrier phase-based relative positioning apparatus comprises a plurality of antennas of which at least one is installed on a mobile unit, means for obtaining at least two pairs of baseline vectors from each pair of the multiple antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with the multiple antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined by calculating the cross product of each pair of the baseline vectors and judging whether the cross product falls in a preset range in which the cross product will fall under normal conditions.
The aforementioned cross product is a vector whose magnitude is equal to the product of the magnitudes of two baseline vectors multiplied by sinxcex8 and direction is perpendicular to a flat plane formed by the two baseline vectors, where xcex8 is the angle between the two baseline vectors. Therefore, if the attitude angles of the flat plane formed by the two baseline vectors fall out of their normal range more greatly as the cross product falls out of its normal range, or if the magnitude of either of the baseline vectors or the baseline length differs from the actual length by more than a specific amount, the integer ambiguity is regarded as being incorrectly determined.
In yet another aspect of the invention, the carrier phase-based relative positioning apparatus judges whether the integer ambiguity has been correctly determined based on whether the attitude of the baseline vectors and the aforementioned cross product fall in preset ranges in which they will fall under normal conditions.
In yet another aspect of the invention, a carrier phase-based relative positioning apparatus comprises a plurality of antennas installed on a body or on a moving body, means for determining the relative positions of each pair of the multiple antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with the multiple antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined based on whether a parameter based on the relative positions of the antennas falls in a preset range in which the parameter will fall under normal conditions.
In yet another aspect of the invention, a carrier phase-based relative positioning apparatus comprises three antennas installed on a body or on a moving body, means for determining the relative positions of each pair of said three antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with said three antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined based on whether a parameter based on the relative positions of the antennas falls in a preset range in which the parameter will fall under normal conditions.
In yet another aspect of the invention, a carrier phase-based relative positioning apparatus comprises two antennas installed on a mobile unit, means for determining the relative positions of said two antennas by receiving radio signals transmitted from a plurality of position-fixing satellites with said two antennas, observing a single difference phase or a double difference phase, and calculating an integer ambiguity of the single difference phase or the double difference phase, and means for judging whether the integer ambiguity has been correctly determined based on whether a parameter based on the relative positions of the antennas falls in a preset range in which the parameter will fall under normal conditions.
This invention serves to improve the reliability of calculated integer ambiguities and shorten the time required for eventually determining one set of correct integer ambiguities from a plurality of candidates. In addition, the invention enables a more reliable judgment on a cycle slip which could occur even after determining correct integer ambiguities.
These and other objects, features and advantages of the invention will become more apparent upon reading the following detailed description in conjunction with the accompanying drawings.